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Statistica Sinica 19 (2009), 1155-1170





ROBUST MODEL SELECTION IN GENERALIZED

LINEAR MODELS


Samuel Müller and A. H. Welsh


University of Sydney and The Australian National University


Abstract: In this paper, we extend to generalized linear models the robust model selection methodology of Müller and Welsh (2005). As in Müller and Welsh (2005), we combine a robust penalized measure of fit to the sample with a robust measure of out of sample predictive ability that is estimated using a post-stratified m-out-of-n bootstrap. The method can be used to compare different estimators (robust and nonrobust) as well as different models. Specialized to linear models, the present methodology improves on Müller and Welsh (2005): we use a new bias-adjusted bootstrap estimator which avoids the need to include an intercept in every model and we establish an essential monotonicity condition more generally.



Key words and phrases: Bootstrap model selection, generalized linear models, paired bootstrap, robust estimation, robust model selection, stratified bootstrap.

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